Multivariate linear mixed for the analysis of multiple responses

Modeling
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1

|I am trying to fit a multivariate linear mixed (MLMM) for the analysis of multiple response |\underbrace{\mathbf{y}}_{qn\times 1} = \boldsymbol{X\beta} + \boldsymbol{\underbrace{Z}_{qn\times qm}\underbrace{\gamma}_{qm\times 1}} + \boldsymbol{\varepsilon},~~ ||\boldsymbol{\gamma}\sim \mathcal{N}(\textbf{0},I_m\otimes\mathbf{G}),~~| ||\boldsymbol{\varepsilon}\sim \mathcal{N}(\textbf{0},I_n\otimes\mathbf{R})

I had the following error messages
“Error in FUN(X[[i]], …) : object ‘iter’ not found
In addition: Warning message:
In system(paste(CXX, ARGS), ignore.stdout = TRUE, ignore.stderr = TRUE) :
‘C:/RTools/rtools40/usr/mingw_/bin/g++’ not found”

Thanks for your reply

data {
  int<lower=0>    N; // number of students
    int<lower=1> q;     //number of responses
   int<lower=1> m;    //number of random effects
    int<lower=1> qm;
    int<lower=1> qN;
    matrix[m,m]   A;           // Identity matrix of size m
    matrix[N,N]   B;           // Identity matrix of size N
  int<lower=1>    p; // number of fixed effects
   matrix[qN,p]    X; // Fixed effects design matrix
  vector[1] Y[qN]; // response variable
  matrix[qN,qm] Z;       //subj ranef design matrix
 
}
transformed data{
  matrix[m,m] LA;
   matrix[N,N] LB;
   LA= cholesky_decompose(A);
  LB = cholesky_decompose(B);
}
  parameters {
  matrix[qm, 1] a_tilde;
  matrix[N, 1] b_tilde;
  vector[p] beta; // fixed effects
  
// Gi matrix
  cholesky_factor_corr[q] L_Omega_G;
  vector<lower=0>[q] L_sigma_G;

// R_i matrix
  cholesky_factor_corr[q] L_Omega_R;
  vector<lower=0>[q] L_sigma_R;
}
transformed parameters {
  matrix[qm,qm] gam;
  matrix[qN,qN] V;
   matrix[qN,qN] R;
      gam = (LA * a_tilde) *diag_pre_multiply(L_sigma_G, L_Omega_G)'; 
       R = (LB * b_tilde) *diag_pre_multiply(L_sigma_R, L_Omega_R)'; 
      V= Z*gam*Z'+R ;
  }
  
model {
     vector[N] mu = X * beta;
    
//E(y)=X*beta var(y)=ZGZ+R
 
    Y ~ multi_normal_cholesky(mu, V);
    to_vector(beta) ~ normal(0, 1);
     to_vector(a_tilde) ~ normal(0, 1);
      to_vector(b_tilde) ~ normal(0, 1);
    L_Omega_G ~ lkj_corr_cholesky(2);
    L_sigma_G ~ cauchy(0, 5);
    L_Omega_R ~ lkj_corr_cholesky(2);
    L_sigma_R ~ cauchy(0, 5);
}
generated quantities {
      cov_matrix[q] G;
    cov_matrix[q] Re;
    corr_matrix[q] corrG;
    corr_matrix[q] corrR;
    G = multiply_lower_tri_self_transpose(diag_pre_multiply(L_sigma_G, L_Omega_G));
    Re = multiply_lower_tri_self_transpose(diag_pre_multiply(L_sigma_R, L_Omega_R));
      corrG = multiply_lower_tri_self_transpose(L_Omega_G);
    corrR = multiply_lower_tri_self_transpose(L_Omega_R);
}
2

You have the whole code encapsulated by model{}, which is not what you’re supposed to do. Remove the first and final lines and it should run.

3

I did remove model{} but same error